Question

Geo-caching is a sport that involves hiking and using clues to find hidden “treasures.” The person who finds the cache is then obliged to leave a treasure for the next person.
Cheyenne and Jacob are geocaching. They are currently hiking on a main trail at a bearing of N 45° E. They determine that the cache should be about 1.5 miles off the trail at a bearing of N 17° E.

If they want to hike to a point 3 miles further along the main trail once they have located the cache, they will hike an additional____miles

1.0
1.8
2.7
3.3

Answer 1

A northeast bearing comes off of the intersection between the y-axis and the x-axis.  This intersection is perpendicular; therefore, the angle formed is 90 degrees.  Subtract the given angles of 45 and 17 and you are left with 28 degrees. So, plug into the equation:

a² = 1.5² + 3² - 2(1.5)(3)·cos(28)

a² = 2.25 + 9 - 9·cos(28)

a² = 11.25 - 9·cos(28)

a² = 11.25 -7.946...

a² = 3.3...

a = 1.8. Pick option 2.